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Tolerances on poset algebras

Bohdan Zelinka (1992)

Mathematica Bohemica

To everz partiallz ordered set a certain groupoid is assigned. A tolerance on it is defined similarlz as a congruence, onlz the requirement of transitivitz is omitted. Some theorems concerning these tolerances are proved.

Unified-like product of monoids and its regularity property

Esra Kırmızı Çetinalp (2024)

Czechoslovak Mathematical Journal

We first define a new monoid construction (called unified-like product O Ω J ) under a unified product O J and the Schützenberger product O J . We investigate whether this algebraic construction defined with operations of the unified and Schützenberger product specifies a monoid or not. Then, we obtain a presentation of this new product for any two monoids. Finally, we define the necessary and sufficient conditions for O Ω J to be regular.

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